彗星雲の起源 - 惑星による微惑星の散乱と集積 - 樋口有理可(1)(2) 小久保英一郎(1) 向井正(2)

Presentation on theme: "彗星雲の起源 - 惑星による微惑星の散乱と集積 - 樋口有理可(1)(2) 小久保英一郎(1) 向井正(2)"— Presentation transcript:

1 彗星雲の起源 - 惑星による微惑星の散乱と集積 - 樋口有理可(1)(2) 小久保英一郎(1) 向井正(2)
I’d like to present my study with the title of ‘’. (1)国立天文台理論天文学研究系 (2)神戸大学自然科学研究科

2 エネルギー(1/a原初軌道)=0付近に彗星が集中
オールト雲 観測： 彗星の原初軌道長半径の逆数と個数の関係 エネルギー(1/a原初軌道)=0付近に彗星が集中 70 軌道傾斜角が一様 50 個数 Oort(1950) 太陽から数万AUの距離に 彗星の巣の存在を提唱 The goal of my study is to clarify the Origin and… I will describe what the comet cloud is later. Toward this goal, I investigate the… Using the results, I build the general theory of the comet cloud formation applicable... -1 1 3 2 4 5 1/a原初軌道 (10-3 AU-1)

3 オールト雲 想像図 半径: ~104AU 彗星総数: ~1013個 総質量: ~100M地球
The goal of my study is to clarify the Origin and… I will describe what the comet cloud is later. Toward this goal, I investigate the… Using the results, I build the general theory of the comet cloud formation applicable...

4 オールト雲の起源 太陽系外起源説 太陽系内起源説 星間空間の天体を捕獲 原始惑星系円盤の外縁部(in situ)で誕生
惑星などと同じく原始惑星系円盤内部から誕生 The goal of my study is to clarify the Origin and… I will describe what the comet cloud is later. Toward this goal, I investigate the… Using the results, I build the general theory of the comet cloud formation applicable...

5 オールト雲形成標準シナリオ 微惑星 形成 惑星摂動 外力 ステージ 惑星の摂動による 遠日点距離の増加 外力の摂動による 近日点距離の増加
太陽 微惑星 惑星摂動 Let me show the standard scenario of the Oort cloud formation. The first stage of the Oort cloud formation is the formation of the planetesimals. When protoplanets or planets are large enough, planetesimals change their orbit and their aphelion distance become large by the planetary perturbation. This is the second stage. Planetesimals with large aphelion distance go to the next stage. In this stage, perihelion distance become large by the external forces and planetesimals leave the planetary region and be a member of the Oort cloud. The external forces are the galactic tide and perturbations of giant molecular clouds and passing stars. In the last stage, the inclination of the planetesimals also become large and realize the spherical structure. 外力

6 研究目的 惑星系 彗星雲 を決定 銀河環境 微惑星形成 惑星摂動 外力 パラメータ オールト雲形成標準シナリオの３ステージ
→　一般の惑星系（彗星雲形成）にも応用可能 パラメータ 惑星系 彗星雲 を決定 Along this standard scenario, I will construct the general theory of the formation of the comet cloud. Using the general theory, if we know the parameters of planetary system and the galactic environment, we can determine the property of the comet cloud of the planetary system. Toward this goal, now I am studying the second stage, planetary perturbation. 銀河環境

7 惑星摂動 衝突 生存 落下 外力 彗星雲天体候補 遠日点距離の増大 のステージへ 惑星による強い摂動を受けた微惑星の運命 惑星系 惑星との
からの脱出 外力 中心星 への 落下 のステージへ In this stage, planetesimals are under the strong gravitational influence of planets. They have four fates. Some planetesimals collide with a planet. They become a part of the planet. Some planetesimals fall onto the central star. While, some planetesimals change their orbital elements largely and escape from the planetary systems. There remain survivors. Some of the escapers and survivors increase their aphelion distance likely, and go to the next stage of the external forces. We can say they are the candidates for the member of the comet cloud. The ratio of these fates may depends on parameters of the planet and planetesimals. To investigate the dependences, I perform numerical calculation focusing on the collision and escape rates. 楕円軌道で 生存 彗星雲天体候補

8 数値計算 モデル 円制限三体問題 数値計算時間 1 ケプラー周期 パラメータ a 軌道長半径 e 離心率 i 軌道傾斜角 微惑星 惑星
モデル 　　　　　　　　円制限三体問題 数値計算時間 ケプラー周期 パラメータ a 軌道長半径 e 離心率 i 軌道傾斜角 微惑星 惑星 ap 軌道長半径　 mp 質量　 I perform the numerical calculation with the model of the circular restricted three-body problem. It means that a planet keeps circular orbit and a planetesimal is a mass less particle. I calculate the orbit of planetesimals for their 1 Kepler period each, with these parameters. The ranges of these parameters are as follows. a e i ap mp 軌道交差領域 +α 0-0.9 0-0.1rad 1-30AU 0.01-1MJ MJ: 木星質量

9 衝突・脱出効率 Ｐcol/esc: 1ケプラー周期あたりの 衝突・脱出確率 ＴＫ :ケプラー周期 ns :微惑星の個数面密度
単位時間当たりの衝突・脱出数の期待値 Ｐcol/esc: 1ケプラー周期あたりの 　　　　　　衝突・脱出確率　 ＴＫ :ケプラー周期 ns :微惑星の個数面密度 2πada :軌道長半径 a　でのリングの面積 amin-amax :衝突・脱出の起こる軌道長半径の領域 To evaluate the rates of collision and escape, I define the efficiency with this formula. The efficiency shows the expected number of collision or escape per time. P is the probability of collision or escape per Kepler period. To make the value par time, it is divided by the Kepler period. ns is the number density of the planetesimals. 2piada is the area of ring with a. And the region from amin to amax, this is the region of a where collision or escape occurs. To obtain the value of efficiency K, I calculate the values of P collision and P escape.

10 P の a への依存 衝突: 領域の両端にピーク 脱出: a とともに増加 衝突 脱出 a (AU) Pcol（％） Pesc（％） e
0.6 i 0.01rad ap 5AU mp 1MJ 衝突: 領域の両端にピーク This is one example of the results of numerical calculation of the probability P. This figure shows the dependence of P on the semimajor axis of planetesimals a. Other parameters are fixed like this. The horizontal axis is a semimajor axis of planetesimals. The vertical axis is P. The top panel shows P of collision. The bottom one shows P of escape’s. These behavior is common to the case of almost all parameters. 脱出: a　とともに増加

11 効率の算出方法 Ｐ: 数値計算結果 amin-amax: 数値計算結果 ns: 最小質量モデル 衝突 脱出 P col (%)
a (AU) P esc (%) P col (%) Ｐ: 数値計算結果 amin-amax: 数値計算結果 ns: 最小質量モデル Using the results of calculation of P, we can calculate the value of the efficiency K. The value of P, and amin and amax are calculated. Each region means the region from amin to amax. In this presentation, I adopt the minimum-mass disk model as the number density of planetesimals. It is proportional to a to the minus 3 over 2. Now we obtain the efficiencies of collision and escape. Let me describe them with simple power laws using the least square fit method.

12 K の e への依存 脱出 衝突 衝突 ∝e-1 脱出 ∝e4 Kcol/esc (AU2 year-1) 0.9
i 0.01rad ap 5AU mp 1MJ 衝突 ∝e-1 This figure shows the dependence of K on the eccentricity of the planetesimals. Other parameters are fixed like this. The horizontal axis is the eccentricity of the planetesimals. The vertical axis is the efficiency K. K collision is almost proportional to e to the minus 1. K escape is almost proportional to e to the 4 when e is larger than 0.4. And there is no escapers with e less than 0.4. 脱出 ∝e4 (e>0.4 only)

13 K の i への依存 脱出 衝突 ∝i-1 衝突 脱出 ∝i-1 Kcol/esc (AU2 year-1) i (rad) e 0.6
ap 5AU mp 1MJ 衝突 ∝i-1 Next, this figure shows the dependence of K on the inclination of the planetesimals. Other parameters are fixed like this. The horizontal axis is the inclination of the planetesimals. Both K collision and K escape are almost proportional to i to the minus 1. 脱出 ∝i-1

14 K の ap への依存 脱出 衝突 ∝ap-2 衝突 脱出 ∝ap-1 Kcol/esc (AU2 year-1) ap (AU) e
0.6 i 0.01rad mp 1MJ 衝突 ∝ap-2 This figure shows the dependence of K on the semimajor axis of the planet. Other parameters are fixed like this. The horizontal axis is the semimajor axis of the planet. K collision is clearly proportional to ap to the minus 2. And K escape is also clearly proportional to ap to the minus 2. 脱出 ∝ap-1

15 K の mp への依存 脱出 衝突 ∝mp4/3 衝突 脱出 ∝mp2 Kcol/esc (AU2 year-1) mp (mJ) e
0.6 i 0.01rad mp 1MJ 衝突 ∝mp4/3 This figure shows the dependence of K on the last parameter, mass of the planet. Other parameters are fixed like this. The horizontal axis is the mass of the planet. K collision is roughly proportional to mp to the 4 over 3. K escape is clearly proportional to mp to the 2. In this case, there is no escape where mp is 0.01 Jupiter mass. 脱出 ∝mp2

16 フィッティング・フォーミュラ 脱出 衝突 e i (rad) Kcol/esc (AU2 year-1)
0.9 Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3 Kesc ≈ 2・10-4×e4・i-1・ap-1・mp2 Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3 Kesc ≈ 2・10-4×e4・i-1・ap-1・mp2 Using these results, I obtain the fitting formulas of K collision and K escape. Here fitting formulas are plotted with the results numerically calculated. The horizontal axis is the semimajor axis of the planet and vertical axis is K. The left panel shows the collisions and the right shows the escapes. The red and the green lines are The magenta and the blue lines are the results with different parameters. All agrees well.

17 フィッティング・フォーミュラ 脱出 脱出 衝突 衝突 Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3
Kesc≈ 2・10-4×e4・i-1・ap-1・mp2 Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3 Kesc ≈ 2・10-4×e4・i-1・ap-1・mp2 脱出 脱出 Kcol/esc (AU2 year-1) Using these results, I obtain the fitting formulas of K collision and K escape. Here fitting formulas are plotted with the results numerically calculated. The horizontal axis is the semimajor axis of the planet and vertical axis is K. The left panel shows the collisions and the right shows the escapes. The red and the green lines are The magenta and the blue lines are the results with different parameters. All agrees well. 衝突 衝突 ap (AU) mp (mJ)　　　

18 まとめ 目的 現在の研究 今後の予定 一般的な彗星雲形成論の構築 微惑星の衝突・脱出効率の微惑星・惑星パラメータ依存性の解明へ向けた数値計算
衝突・脱出効率のフィッティング・フォーミュラの導出 今後の予定 Now, let me summarize my presentation. Toward this goal, I investigated the… Using the results, I obtained the fitting formula… 衝突・脱出効率の解析的導出 次の外力のステージの研究 一般的な系外惑星系への応用

19 P の a への依存 衝突: 領域の両端にピーク 脱出: a とともに増加 衝突 脱出 a (AU) Pcol（％） Pesc（％） e
0.7,0.8,0.9 i 0.0rad ap 5AU mp 1MJ 衝突: 領域の両端にピーク This is one example of the results of numerical calculation of the probability P. This figure shows the dependence of P on the semimajor axis of planetesimals a. Other parameters are fixed like this. The horizontal axis is a semimajor axis of planetesimals. The vertical axis is P. The top panel shows P of collision. The bottom one shows P of escape’s. These behavior is common to the case of almost all parameters. 脱出: a　とともに増加

20 フィッティング・フォーミュラ e=0.6 e=0.9 衝突 脱出 Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3
i=0.01rad mp=1mJ e=0.6 e=0.9 Kcol (year-1) Kesc (year-1) ap (AU) 衝突 　　 脱出 Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3 Kesc ≈ 2・10-4×e4・i-1・ap-1・mp2 Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3 Kesc≈ 2・10-4×e4・i-1・ap-1・mp2 Using these results, I obtain the fitting formulas of K collision and K escape. Here fitting formulas are plotted with the results numerically calculated. The horizontal axis is the semimajor axis of the planet and vertical axis is K. The left panel shows the collisions and the right shows the escapes. The red and the green lines are The magenta and the blue lines are the results with different parameters. All agrees well.

21 フィッティング・フォーミュラ Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3
i=0.01rad ap=5AU Kcol ≈ 8・10-6×e-1・i-1・ap-2・mp4/3 Kesc ≈ 2・10-4×e4・i-1・ap-1・mp2 e=0.6 e=0.9 e=0.6 e=0.9 Kcol (year-1) Kesc (year-1) Next, the horizontal axis is mass of the planet. In these figures, the fitting formulas and the numerical results do not agree so well where mp is small. In this region, the accuracy of the numerical calculations was not enough because the probabilities of collision and escape are very small with small mp. 衝突 　　　　脱出 mp (mJ) mp (mJ)